Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-5y &= 3 \\ 2x+8y &= -7\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -8y-7$ Divide both sides by $2$ to isolate $x$ $x = {-4y - \dfrac{7}{2}}$ Substitute this expression for $x$ in the first equation. $-({-4y - \dfrac{7}{2}}) - 5y = 3$ $4y + \dfrac{7}{2} - 5y = 3$ Simplify by combining terms, then solve for $y$ $-1y + \dfrac{7}{2} = 3$ $-1y = -\dfrac{1}{2}$ $y = \dfrac{1}{2}$ Substitute $\dfrac{1}{2}$ for $y$ in the top equation. $-x-5( \dfrac{1}{2}) = 3$ $-x-\dfrac{5}{2} = 3$ $-x = \dfrac{11}{2}$ $x = -\dfrac{11}{2}$ The solution is $\enspace x = -\dfrac{11}{2}, \enspace y = \dfrac{1}{2}$.